Problem: In winter, the price of apples suddenly went up by $\$0.75$ per pound. Sam bought $3$ pounds of apples at the new price for a total of $\$5.88$. Write an equation to determine the original price per pound $(p)$. Find the original price per pound. $\$$
Answer: Let $p$ be the original price per pound of apples. The new price is $p+{0.75}$ dollars per pound. Sam bought $3$ pounds of apples. Sam's total cost was $3(p+0.75)$. Since his total cost was $\$5.88$, let's set this equal to $5.88$ : $ 3(p+0.75)=5.88$ Now, let's solve the equation to find the original price per pound $(p)$. $\begin{aligned}3(p+0.75)&=5.88\\&\\ \dfrac{3(p+{0.75})}{3}&=\dfrac{5.88}{3}&&\text{divide both sides by $3$}\\ \\ p+{0.75}&=1.96\\ \\ p+{0.75}{-0.75}&=1.96{-0.75}&&{\text{subtract }} {0.75} \text{ from both sides}\\ \\ p&=1.21\end{aligned}$ The equation is $3(p+0.75)=5.88$. The original price of the apples was $\$1.21$ per pound.